Actually the stated reason is plausible. It's not that it was any great secret. Close estimates were on the interweb - Wikipedia, Global Security, Federation of Atomic Scientists, and nuclearweaponarchive U.S. Nuclear Weapon Enduring Stockpile Last changed 31 August 2007
At the beginning of 2007 the U.S. nuclear arsenal was composed of eight types of nuclear warheads (in thirteen variant mods) that are operationally deployed, with an estiamted count of 5,736 active stockpile warheads.The information was there for anyone who wanted it as background.
This announcment only makes it available to people too stupid to use Google. And what do you think people believing "galvanise efforts to rid the world of nuclear weapons" is feasible are?
You are, of course, absolutely correct.
However, the naif in the White House thinks that revealing how many warheads we have is going to do anything to encourage people to reduce their stockpiles.